This article is from the LAN Mail Protocols FAQ, by John Wobus firstname.lastname@example.org with numerous contributions by others.
The IMAP family is similar to the POP family, but also gives clients a
way to do string searches through mail that still resides on the
server. This is designed to allow the desktop computer to be more
selective as to which mail will be transferred. Among other features
IMAP also allows mail on the server to be placed in server-resident
folders. The POP protocols, on the other hand, are designed for
simpler server software.
IMAP2 is used quite a bit. IMAP3 is an incompatible offshoot that has
not been implemented much. IMAP2bis is an extension of IMAP2 which is
still in use. Among other things, it made servers cognizant of the
MIME-structure of a message. IMAP4 is a refinement and extension of
IMAP2bis, and while it may still be in use somewhere, IMAP4rev1, which
makes necessary corrections to a few problems with IMAP4 as
documented, has replaced it (it was given a new designation to allow
you to demand it by name) and it is suggested that IMAP4-non-rev1
support be dropped from servers & clients in favor of IMAP4rev1.
IMAP4(rev1) also extends IMAP to have many other features including
some of those associated with DMSP.